When performing working or machining to form a free-form curved surface on a work such as die machining, the working or machining is in many instances conducted by mounting a ball end mill or the like on an NC milling machine or machining center. After such working or machining is performed, cutting tool marks are caused to remain on the thus-finished die. Hence, it cannot be used as a die without any further machining or treatment. This will next be described with reference to FIG. 2.
FIG. 2 is a perspective view illustrating cutting work by a ball end mill. In the drawing, there are shown a table 1 of a working machine, a work 2 fixedly held on the table 1, and a ball end mill 3 for cutting the work 2. Machining of the work by such a working machine is performed in the following manner. Namely, the work 2 is cut by shifting the table 1 in a direction indicated by the arrow A while moving the ball end mill 3 up and down. Upon completion of the cutting in the direction A, the table 1 is shifted a little bit in a direction indicated by the arrow B (pick-feed) and cutting is again performed in the direction A. These operations are repeated successively. In this case, cutting tool marks 4 are caused to remain due to the pick-feed on the surface of the work 2. Thus, the work 2 machined in such a way cannot be used as a final product. It is therefore necessary to add a further step to remove the cutting tool marks 4 in order to convert the above-machined work 2 into a final product. Incidentally, the above-described cutting tool marks 4 are left with a substantially equal interval on the surface of the work 2 and their heights range approximately from 0.1 mm to 0.2 mm. It should be noted that the cutting tool marks 4 shown in FIGS. 2 and 3 are exaggerated to facilitate their understanding. The heights of these cutting tool marks 4 must be reduced to at least 1 .mu.m to 0.5 .mu.m.
Conventionally, the above-machined work was manually worked with a shafted grinder held by a hand. Assuming now that one would employ the prior art technique and perform it mechanically, the following machine may be contemplated.
FIG. 3 is a perspective view showing conventional grinding work, in which like elements of structure to those shown in FIG. 2 will be designated by like reference numerals. Numeral 5 indicates a shafted grinder which is attached to a working machine. The profile of the work is in advance stored in a computer or the like and, on the basis of the thus-stored information, cutting tool marks 4 are traced by the shafted grinder. However, as mentioned, above, the heights of the cutting tool marks 4 are as low as several tenths millimeter or so, and their sizes and shapes are irregular. Thus, it is impossible to finish the surface of the work into any sufficiently smooth surface if one relies upon the accuracy achieved merely by storing the profile of the work 2 in a computer. Namely, the working tool may cut the work 2 too deep at certain parts and may be detached from the work 2 at some other parts.
The above method is accompanied by another serious drawback. It cannot be applied unless profile data of each work are available in advance. It has thus been usual to carry out the removal of cutting tool marks 4 manually, because the automatic grinding machine conceivable from the prior art is accompanied by such serious drawbacks as mentioned above, and no other suitable automatic grinding machine is available. This applies not only to the above-described machining work, but also to general profile-machining work. Such machining work has prevented full automation of machining steps, resulting in the need for lots of man power and time.
In order to solve such problems of the prior art techniques and enable automatic machining, the present inventors conceived that the above machining could be achieved by machining the surface of a work while pressing a working tool at a constant pressing force against the surface of the work and tracing the profile of the surface of the work. With a view toward materializing the above idea, the following study was carried out. The study will next be described with reference to FIGS. 4(a), 4(b) and 4(c).
FIGS. 4(a), 4(b) and 4(c) are respectively a front view, plan view and side view of a working tool and work. It is necessary to control the relative positional relationship between the working tool and the work in order to press the working tool at a constant pressing force against the work as mentioned above. For this purpose, it is necessary to preset coordinate axes. FIGS. 4(a) through 4(c) show such coordinate axes. In the figures, there are shown a table 1, a work 2, and a working tool 6. The working tool 6 has a center O of rotation, and it has a profile which contains a spherical surface having a radius r. Numeral 7a indicates an arm for rotating the working tool 6, and numeral 7b is a support arm. Numeral 8 designates a load sensor connected rigidly to the support arm 7b, and numeral 9 is a drive source for rotating the arm 7a. The drive source 9 is attached rigidly to one end of the load sensor 8, which one end is opposite to the end to which the support arm 7b is rigidly connected. A variety of load sensors have been known for the load sensor 8. It is however desirable to use a load sensor of the type proposed in Japanese Patent Laid-Open No. 62497/1985 (which corresponds to U.S. patent application Ser. No. 605,212 filed Apr. 30, 1984 now U.S. Pat. No. 4,268,745). The support arm 7b is coupled to an unillustrated main body of a working machine and is rotated and displaced three-dimensionally. As illustrated in the figures, a coordinate system X-Y-Z has been established with a suitable portion Om of the main body of the working machine being as an origin, while a coordinate system x-y-z is established with the center O of rotation of the working tool 6 being as its origin. Letter T indicates a point of action (working point) of the working tool 6 on the work 2, whereas letter F indicates a working reaction force exerted on the working tool 6. Incidentally, the table 1 is, in most general forms, turnable about any of three axes which are not contained in the same plane. This function of the table is however omitted in the figures.
Description will next be made of grinding work where the surface of the work 2 is flat. FIG. 5 is an enlarged front view of the working tool 6 and the work 2. In the figure, there are shown the work 2, the working tool 6, the working point T, the working reaction force F, and the flat surface P.sub.t1 on the work 2. Let's now establish a force coordinate system .xi.-.zeta., which includes the working point T as its origin, as shown in the figure. Namely, the .zeta.-axis is placed as a line passing through the working point T and the center O of the working tool 6, while the .xi.-axis is defined as an intersecting line between the plane P.sub.t1, which is perpendicular to the .zeta.-axis, and a plane defined by the feeding direction (the direction of the x-axis) of the working tool 6 and the .zeta.-axis. Since the coordinate system has been established in the above-mentioned manner, the .zeta.-axis is coincided with the z-axis, and the .xi.-axis extends in parallel with the x-axis. The coordinate system .xi.-.zeta. has been established in the above-mentioned manner in order to handle the .xi.-axis force component F.sub..xi. of the working reaction force F as the tangential force component of the grinding work, the .zeta.-axis force component F.sub..zeta. as a normal force component, and an angle .psi.(.psi.=tan.sup.-1 F.xi./F.zeta.) as the direction of the reaction force. It is hence possible to keep working conditions under optimum conditions by controlling these tangential force component F.sub.z, normal force component F.sub..zeta. and angle .psi. at suitable values.
By the way, in grinding work, the magnitude F and direction .psi. of the working reaction force change in various ways. Conditions under which the grinding efficiency and the quality of finishing are optimized may be achieved by controlling the magnitude F and direction .psi. of the working reaction force to their respective optimum values F.sub.0, .psi..sub.0. In view of this, a control system shown in FIG. 6 may be contemplated.
FIG. 6 is a system diagram of a working machine, in which the working machine is applied to a flat work surface. In the figure, there are shown a working tool/work system 10 composed of the working tool 6, the table 1, the work 2, and the like, a load sensor 8 shown in FIGS. 4(a) and 4(b), and a drive and control system 11 for reach of the individual axes. The drive and control systems 11 for the respective axes are composed of drive and control systems, that are adapted to control the drive of the working tool 6 in the directions of the respective axes on the basis of the X-Y-Z coordinate system, and other drive and control systems for controlling the tiltings (.theta..sub.1, .theta..sub.2, .theta..sub.3) about the three axes so as to control the relative positions of the working tool 6 and the work 2. The drive and control systems 11 drive and control the working tool 6 and/or the table 1 so as to establish desired relative positions between the working tool 6 and the work 2. Designated at numeral 12 is a controlling and computing unit for performing prescribed operations in accordance with each detection signal from the load sensor 8.
When the working tool 6 is being driven in the direction x as illustrated in FIG. 5, components F.sub.x (which is equal to the force component F.sub..xi. in this case) and F.sub.z (which is equal to the force component F.sub..zeta.) of a reaction force exerted at the working point T are detected by the load sensor 8, and the detection signals of the load sensor 8 are output to the controlling and computing unit 12. The controlling and computing unit 12 then computes, based on the detection signals, such desirable values X,Y of the relative positions X,Y between the working tool 6 and the work 2 that the magnitude F (F=.sqroot.F.sub..xi..sup.2 +F.sub..zeta..sup.2 =.sqroot.F.sub.x.sup.2 +F.sub.z.sup.2) and direction .psi. (.psi.=tan.sup.-1 F.xi./F.zeta.=tan.sup.-1 F.sub.x /F.sub.z) should become their respective optimum values F.sub.0 and .psi..sub.0. The values X, Z computed at the controlling and computing unit 12 are then input to the drive and control systems 11 for the respective axes. In accordance with the values X, Z, the drive and control systems 11 for the respective axes change the relative positions in the working tool/work system 10 to new relative positions X,Z. As a result, the magnitude F and the direction .psi. of the reaction force are maintained respectively at their optimum values F.sub.0 and .psi..sub.0. Hence, the working tool 6 is pressed under a constant pressing force against the work 2, thereby to permitting automatic machining without developing breakage or abrupt wearing on the working tool 6 while maintaining the optimum working conditions.
Here, the operation at the controlling and computing unit 12 will be described in further detail. It is dependent on the material of the work 2 and the material, shape, rotation speed, rotating direction, etc. of the working tool 6 how the working reaction force changes in accordance with a varied depth of cut and a feeding speed. Namely, the working reaction force is not constant. Therefore, it is not possible to show the computing means of the controlling and computing unit 12 in a general form. According to findings obtained through experiments, the direction .psi. of the working reaction force remains substantially at a constant value .psi..sub.0 in the neighbourhood of practical feeding speeds and depths of cut. However, for such practical feeding speeds and depths of cut, only the magnitude F of the working reaction force varies in accordance with the details of each grinding specification as values F', F" as shown by broken lines in FIG. 5. Therefore, the working reaction force can be controlled if either one of the values F.sub..zeta. and F.sub..xi., which are components of the working reaction force, is detected and the thus-detected value F.sub..zeta. or F.sub..xi. is controlled to the .zeta.-axis force component F.sub..xi..sbsb.0 of the above-described optimum value F.sub.0. Based on the above concept, the control algorithm of the controlling and computing unit 12 will hereinafter be described.
The controlling and computing unit 12 may be adapted to perform an operation in such a way that, by paying attention for example only to the normal force component F.sub..zeta., a value capable of controlling the relative positions of the working tool 6 and the work 2 in the direction of the .zeta.-axis (which is equal to the direction of the z-axis in this case) so as to make the force component F.sub..zeta. approach the optimum value F.sub..zeta..sbsb.0 is calculated. For this purpose, the speed v.sub..zeta. in the direction of the .zeta.-axis may be chosen in such a way that it either increases or decreases depending on the difference .DELTA.F.sub..zeta. (.DELTA.F.sub..zeta. =F.sub..zeta. -F.sub..zeta.0) between the force component F.sub..zeta. and the optimum value F.sub..zeta..sbsb.0. The speed v.sub..zeta. may for example be chosen to equal A.sub.1 (F.sub..zeta. -F.sub..zeta.0), in which A.sub.1 is a positive constant, and the optimum value F.sub..zeta.0 is represented by F.sub.0 cos .psi..sub.0. Supposing that the speed v.sub..xi. in the direction of the .xi.-axis, which is equivalent to the feeding direction, is always kept at a constant feeding speed v.sub.t, the velocities v.sub.x, v.sub.z in the direction of the x-axis and z-axis are respectively represented as follows: ##EQU1## Furthermore, supposing that the advancing direction of the central point O of the working tool 6 is at an angle .phi. as measured from the positive direction of the x-axis, the angle can be represented as follow: ##EQU2## Since the x-axis and z-axis are respectively parallel to the coordinate axes X and Z of the main body of the working machine, the values X and Z may be calculated on the basis of the outputs from the controlling and computing unit 12 in the above case while supposing X=v.sub.x and Z=v.sub.z.
The above-described control algorithm has been given merely by way of example. Various other methods may also be contemplated. Although the speed v.sub..xi. in the feeding direction is set as the constant value v.sub.f in the above-described method, it may also be possible to employ such a way of thinking that the absolute value of speed of the working tool 6 at each moment upon proceeding with machining while moving the working tool 6 slightly up and down in accordance with the profile of the work 2 is chosen as an ideal feeding speed v.sub.f (which may be determined experimentally). In this case, the speeds v.sub.z, v.sub.x may be chosen as follows: ##EQU3## When the speeds v.sub.z, v.sub.x are chosen as described above, the angle .phi. can be expressed as follow: ##EQU4##
The above-described control algorithm of the controlling and computing unit 12 is to perform continuous control in the direction of the .zeta.-axis in accordance with the difference .DELTA.F.sub..zeta. between the force component F.sub..zeta. and the optimum value F.sub..zeta.0. The following means may however, be employed in order to further simplify the operation and control in the controlling and computing unit 12. Such means will next be described with reference to a block diagram depicted in FIG. 7.
FIG. 7 is an enlarged front view of the working tool 6 and the work 2, for describing the operation of the controlling and computing unit. In the figure, forces, angle, points, axes, etc. similar to those shown in FIG. 5 are identified by like reference letters. D.sub.1 -D.sub.5 are vectors indicating the magnitudes and directions of speeds preset with the point O being a center. In this simplified means, the degrees of difference between the detected force component F.sub..zeta. and its optimum value F.sub..zeta.0 are classified into five ranges, and the velocity in each range with which the working tool 6 should move to let F.sub..zeta. coincide with F.sub..zeta.0 is made correspond to each one of the five vectors D.sub.1 -D.sub.5. Thus an x-axis component v.sub.x and a z-axis component v.sub.z which the controlling and computing unit 12 should output are gained from each vector. Velocity components to be obtained when the five ranges are rendered corresponding to the vectors respectively may be summarized as shown in Table 1.
TABLE 1 ______________________________________ Direction Value F.sub..zeta. .phi. D.sub.i v.sub.x v.sub.z ______________________________________ F.sub..zeta. &lt; 0.4F.sub..zeta.0 -90.degree. D.sub.1 0 -v.sub.0 0.4F.sub..zeta.0 .ltoreq. F.sub..zeta. &lt; 0.8F.sub..zeta.0 -45.degree. D.sub.2 v.sub.0 -v.sub.0 0.8F.sub..zeta.0 .ltoreq. F.sub..zeta. &lt; 1.2F.sub..zeta.0 0.degree. D.sub.3 v.sub.0 0 1.2F.sub..zeta.0 .ltoreq. F.sub..zeta. &lt; 1.6F.sub..zeta.0 45.degree. D.sub.4 v.sub.0 v.sub.0 1.6F.sub..zeta.0 .ltoreq. F.sub..zeta. 90.degree. D.sub.5 0 v.sub.0 ______________________________________
In Table 1, the value v.sub.0 is a constant value which is chosen from working specification and is close to the ideal feeding speed v.sub.f. In the above means, the angle .phi. is limited discretely to five directions, unlike the said means for performing continuous control in the direction of the .zeta.-axis. Furthermore, the speeds v.sub.x, v.sub.y are limited in advance to the three values 0, v.sub.0 and -v.sub.0. Therefore, it may be expected that the control may somewhat lack smoothness. However, the cycle time of operations is a very small value. Accordingly, no inconvenience or problem will practically arise even when control is performed by such means. In digital control making use of a microcomputer, the outputs v.sub.x, v.sub.z may each require only three levels which correspond to the values 0, v.sub.0 and -v.sub.0. Thus, the computing system can be simplified to a significant extent. The constants which are employed in Table 1 to classify the values F.sub..zeta. are not necessarily limited to the values given in Table 1, but may stand for a variety of suitable values.
The foregoing is the matter studied by the present inventors. In the above-described manner, it will become possible to press the working tool 6 at a constant pressing force against the surface of the work and to perform automatic machining without developing breakage or abrupt wearing on the working tool 6 while maintaining optimum machining conditions. However, the above control is fundamentally effective only where the surface of the work 2 is a flat surface. It is accompanied by a problem that it cannot be successfully applied when the surface of the work 2 is a curved-surface.